Study Tools

1D Motion

Introduction to One-dimensional Motion

Position Functions in One Dimension

Terms

Kinematics
-
Kinematics is concerned with describing the way in which objects move.

Displacement
-
An objects total change in position. If a man runs around an oval 400 meter
track, stopping at the precise location he began, though he ran a distance of
400 meters, his total displacement was 0.

Dynamics
-
Dynamics focuses on understanding why objects move the way they do.

Reference frame
-
The coordinate system with respect to which motion is being described.

Speed
-
A measure of how fast an object is moving.

Average velocity
-
The time-average of the velocity function over a specified time-interval.
(See formula below.)

Instantaneous velocity
-
The value of the velocity function at a particular instant in time. (See
formula below.)

Gravitational acceleration
-
The graviational acceleration of objects near the earth's surface is the same
for all objects regardless of mass and is given by the number
g = 9.8m/s2
.

Scalar-valued function
-
A function that outputs scalars (regular
numbers). Most common functions that you are probably familiar with are
scalar-valued functions.

Vector-valued function
-
A function that outputs vectors. This means that
while the domain of the function may consist of
scalars, the values in the range are all vectors.

Position function
-
A position function can be either scalar-valued (for motion in one
dimension) or vector-valued (for motion in two or three dimensions). At
each point in time its value represents the position of an object at that time.

Velocity function
-
This function is the time-derivative of the position function, and
gives the velocity of an object at each point in time.

Acceleration function
-
This function is the time-derivative of the velocity function, and the
second time-derivative of the position function. It gives the value of the
acceleration of an object at each point in time.

Time-derivative
-
The time-derivative of a function is a new function whose value at each
point represents the rate of change of the original function with respect
to time.

Simple harmonic motion
-
Periodic motion that can be described by special types of position functions.
Examples of simple harmonic motion include an object moving in a circle and a
ball bouncing up and down on a spring.

Formulae

The average velocity for an object with position function
x(t)
over the
time interval
(t0, t1)
.

vavg =

The instantaneous velocity at time
t
for an object with position function
x(t)
.